In the speech on Tuesday, May said the UK would seek to reach a new, unspecified customs agreement, but would not remain in the single market.
One key Brexit aim, she said, was to control the number of people entering the UK from the EU.
She also warned the UK would walk away from what she called a "bad deal" for Britain.
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The plan comes complete with 12 goals, including an assurance that security cooperation with the EU will continue.
May also said the country could seek trade deals across the globe, and MPs would get a vote on the final Brexit deal.
MEPs will vote on the final deal with the EU before it comes into force.
Parliament's chief Brexit negotiator, Guy Verhofstadt, reacted bullishly after May confirmed the UK will be leaving the single market to regain control of its immigration policies as she set out her long-awaited vision.
He signalled he would be playing hardball - dismissing an à la carte option.
May's much-awaited speech comes with the UK edging ever closer to triggering article 50, the process which will pave the way for the country to exit the EU.
Full talks will only start when this process starts at the end of March.
Responding to May's Brexit speech, European Council President Donald Tusk said it was a sad day but that May had made a "more realistic announcement" on Brexit and the EU was now ready to start starts.
Further comment came from Glenis Willmott, Labour's leader in the European Parliament, who said, "So now we know: Theresa May has given up on the single market before negotiations have even begun, whatever the cost - the cost in jobs, the cost in trade, the cost to our economy.
"Britain is leaving the EU, but the choices about how we leave will sit with May and the government - and this looks like a Tory plan that will make most people poorer.
"And despite all of this, we still don't have clarity on what she actually wants to achieve in terms of our future trading relationship with Europe. So despite the all the talk we still face uncertainty, putting even more jobs at risk."
From across the political divide, Ashley Fox, leader of Conservative MEPs in Parliament, welcomed May's speech, saying, "The Prime Minister has today has laid out clearly and firmly how Britain will approach negotiations over our departure from the EU.
"In doing so she has swept away misleading definitions such as hard and soft Brexit and ruled out making-do with an ill-fitting, off the peg arrangement. Instead we are going to move beyond binary choices and seek a bespoke deal that works for both the UK and the remaining members of the EU.
"Everyone now knows where Britain stands and this clarity should enable meaningful talks to commence as soon as article 50 is submitted."
Fox added, "We will deliver what the British people instructed us to do. Conservative MEPs stand ready to assist the process of securing an outcome that allows Britain to flourish as a prosperous international trading nation while remaining a close partner and reliable ally of the EU."
His party colleague, Vicky Ford, who chairs Parliament's internal market committee, said May's speech offers both the EU and UK an opportunity to move beyond simplistic 'in or out' scenarios on the single market and customs union, and instead focus on finding a new partnership.
The Tory MEP said, "We now need to move beyond the simplistic and binary view that we must either be in or out of the single market and customs union. May's speech now sets the scene for the kind of detailed and nuanced discussion that is needed once article 50 is triggered.
"Many countries have preferential access to the single market and an enhanced relationship on customs matters. None of the existing models fit perfectly with the UK's position, and the extent to which the economic ties between the UK and the rest of Europe have become intertwined.
"It is in the interest of all parties to find an arrangement that maximises market access and maintains close regulatory cooperation.
"This new relationship needs to work practically as well as politically. I hope that moving past this binary 'in or out' discussion will mean all negotiators can now roll up their sleeves and start focusing on the specific details of a new partnership that benefits both sides."
Of the programme outlined by May, Ukip leader Paul Nuttall said, "Some of it did sound like a Ukip conference speech and she's now applying some of the things that we've been talking about for many, many years.
"I am concerned that what we're getting is some sort of slow-motion Brexit where she is speaking about interim measures, or a transitional period, which will only begin after April 2019.
"She has given no end date to these transitional measures. I challenge the Prime Minister; let's have this all done and clean before the next general election in 2020. On a positive note I would probably give a 7/10 today.
"Good marks for saying we are leaving the EU's single market and stopping mass immigration. However, he vital issues of leaving the European Court of Human Rights and taking back control of our fishing waters have been left out completely.
"As justice and home affairs minister, May always talked tough but failed to deliver. I challenge her to change the habit of a political lifetime and actually deliver this time. And I mean on time and in full respond."
The set piece speech was also welcomed by Open Europe, a UK-based think tank, whose spokesperson said, "The UK's objectives are now clearer - the best possible comprehensive UK-EU free trade agreement, as well as a new strategic partnership with horizontal cooperation on issues such as security and law-enforcement, as well as foreign policy and defence, and a couture deal on customs preserving some common standards but allowing the UK to strike independent trade deals."
He added, "By acknowledging the importance of phasing Brexit to protect business from cliff edges, and focusing on ends rather than means, May is giving herself sensible flexibility and wiggle room.
"Negotiations - as she presciently said - require compromise. We will see how EU leaders, as well as governments and opposition figures across Europe respond."
Further reaction came from the European University Association (EUA), which said May "showed appreciation" for the UK's academic and scientific communities.
Thomas Jorgensen, EUA's senior policy coordinator and main staff expert on Brexit, said, "She welcomed agreement to continue collaborating with European partners on major initiatives in science, research and technology and did not exclude paying into European programmes.
"EUA stands behind this viewpoint and sincerely hopes this will translate into the UK's continued association to the EU's framework programmes for research. The Association also hopes this focus will carry a promise for continued UK association to Erasmus+, the EU's highly-successful student mobility programme."
But global shipping expert Fastlane International said May's plan to abandon the common external tariff "will cost UK businesses £44bn and throw the baby out with the bath water."
It could also lead to a 20 per cent rise in the cost of exports, warned the group.